# Questions tagged [kerr-metric]

The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.

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### How to derive Smarr formula for Kerr Black Hole?

Following is the Smarr formula for Kerr Black Hole $$M=\frac{\kappa A}{4\pi}+2 \Omega J$$ where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area ...
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### Quantum field expansion and bogoliubov coefficients in the interior of a rotating black hole

I am trying to quantize a real scalar field in the interior of a rotating black hole (3+1 D, asymptotically flat). My question is regarding the modes of the radial part of the equation (obtained after ...
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### How does loop quantum gravity handle spacetimes which aren't globally hyperbolic, like the Kerr metric?

Loop quantum gravity assumes spacetime is globally hyperbolic. However, the interior of a Kerr black hole isn't globally hyperbolic, containing closed timelike curves. So, how are Kerr black holes ...
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### Checking inverse metric and Christoffel symbols for the Kerr metric against references

I am trying to cross-check the Christoffel symbols and other very laborious geometric components in several metrics. In particular the Kerr metric is notoriously complex and results in expressions ...
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### Can a Kerr black hole become super-extremal?

Let's assume there is a large Kerr black hole, which is almost extremal and would become extremal with the addition of a small amount of mass $M$ with spin $J$ to make the final $J=M$. What if this ...
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### What happens to the ring singularities when two Kerr black holes merge?

Imagine two Kerr black holes with ring singularities oriented in different axes (e.g. one horizontal and the other one vertical). If they merge, what will happen to these singularities? Will they form ...
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### What are spinning black holes orbiting?

I have seen depictions of spinning black holes with the "singularity" spinning around a center of rotation in a flat plane, or moving around an imaginary sphere. Is there anything in the ...
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### Is the Schwarzschild singularity a limit of the Kerr singularity?

In a Schwarzschild black hole, the singularity is spacelike. In a Kerr black hole, it is timelike. Is there any continuous transformation between those solutions? Can the Schwarzschild solution be ...
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### Can ring singularities form a Hopf link?

Can ring singularities form a Hopf link?
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### Why domain of Kerr black hole includes negative values for $r$ coordinate?

I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two ...
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### Does someone falling into a spinning black hole see the end of the universe?

It is well known that if you fall into the Schwarzschild black hole you cannot see the entirety of the outside spacetime since there are photons which cannot catch up with you before you reach the ...
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### Angular velocity of stationary observer

I am studying Kerr metric in Boyer Lindquist coordinates and having trouble in understanding the components of angular velocity of stationary observer with constant r and $\theta$ motion w.r.t ...
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### Significance of simultaneous transformation of $t$ and $\phi$ in kerr metric

The Kerr metric in Boyer-Lindquist coordinate is invariant under simultaneous transformations $t \rightarrow -t$ and $\phi \rightarrow -\phi$ but not invariant if we apply one transformation only. ...
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### Perimeter of Kerr's event horizon

We can compute the "proper circumference" of the Schwarzschild event horizon integrating its line element along its perimeter at a fixed $t$. This would be the minimum length of a rope that ...
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### Is it possible to refind entry trajectory after leaving a rotating black hole?

I'm asking about the case where an infalling object travels a path right through a rotating black hole, intact. I want to provide a simple parallel for the purposes of question clarity: A horse can ...
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### What actually is Boyer-Lindquist coordinates?

I want to know the difference between spherical and Boyer-Lindquist coordinates. Don't they both use $r, \theta, \phi$ parameters? I've searched books and sources on the internet and there's none that ...
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### Gray body factors of PBH's - radial equation approximation (Page 1976)

I'm deriving the results of the Page paper: "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole*" (https://doi.org/10.1103/PhysRevD.13.198). At ...
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### What would Hawking radiation look like from inside the event horizon?

Let’s say you fell into a rotating black hole, the inner horizon of the black hole is an infinite blue shift surface, so you should be able to observe events from the arbitrarily far future before ...
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### Why are there two interior regions in this diagram?

Why are there two interior regions in this diagram? There seems to be two inner horizons, and two wormhole regions. Where do the two such regions comes from? What determines which reason someone falls ...
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### Where do the other black holes in this diagram come from?

In this Penrose diagram for a charged/Rotating black hole, once your in the new universe you can continue onward to an infinite sequence of black holes/white holes. So I'm asking, where do those black ...
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### Blandford-Znajek process - energy flow reverse and other questions

In the original BZ paper [1] from 1977, the authors invoke a number of facts and conclusions that I do not quite follow. In the hope that someone has read it and was able to grasp all the details, I ...
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### What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and angular momentum approach each other? What would happen to the black holes in question?
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### How can I make the Kerr black hole surfaces scale well in my diagrams?

I've read that the equatorial radius of the ergosphere of a rotating black hole is the Schwarzschild radius. But in this animation made in natural units by Yukterez it doesn't apply. I then used ...